In summary, the use of the Fisher information as a sensitivity measure has wide application across science and engineering. Nevertheless, practical issues can hinder the translation of the sensitivity information into actionable decisions. In this paper, we propose a new approach using the symplectic decomposition to extract the Fisher sensitivity information. The symplectic decomposition utilises Williamson’s theorem [1]}, [2]} which is a key theorem in Gaussian quantum information theory [3]}. Originated from Hamiltonian mechanics, the symplectic transformations preserve Hamilton’s equations in phase space [4]}. In analogy to the conjugate coordinates for the phase space, i.e. position and momentum, we regard the input parameters as conjugate pairs and use symplectic matrix for the decomposition of the Fisher information matrix (FIM). The resulted symplectic eigenvalues of large magnitude, and the corresponding symplectic eigenvectors of the FIM, then reveal the most sensitive two-parameter pairs.
